SFB 303 Discussion Paper No. B - 37
Author: Dierker, Hildegard
Title: Existence of Nash Equilibrium in Pure Strategies in an Oligopoly with Price Setting Firms
Abstract: Consider an oligopoly model with differentiated products and with a fixed, finite number of price setting
firms. We assume that cost functions are convex and demand is derived from a consumption sector with a
continuum of consumers. We study existence of Nash equilibrium in pure strategies by imposing assumptions on
the distribution of consumers' wealth and tastes rather than postulating a concave profit function. We employ a
result of W. Hildenbrand's saying that demand for a commodity is a decreasing function, if the wealth
distributions has a falling density. The necessary second order conditions on aggregate demand are derived from
assumptions on the distribution of consumers' tastes which imply that preferences are price-dispersed.
Creation-Date: January 1986
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